In [FS1] we announced a precise asymptotic formula for the ground-state energy of a non-relativistic atom. The purpose of this paper is to establish an elementary inequality that plays a crucial role in our proof of that formula. The inequality concerns the Thomas-Fermi potentialVTF = -y(ar) / r, a > 0, where y(r) is defined as the solution of⎧ y''(x) = x-1/2y3/2(x),⎨ y(0) = 1,⎩ y(∞) = 0.
Large-scale systems, such as computer and telecommunication networks, complex control systems and many others, operate in inherently parallel environments. It follows that there are many opportunities to admit parallelism into both the algorithm of control implementation and simulation of the system operation considered. The paper addresses issues associated with the application of parallel discrete event simulation (PDES). We discuss the PDES terminology and methodology. Particular attention is...
The problem considered concerns data reduction for machine learning. Data reduction aims at deciding which features and instances from the training set should be retained for further use during the learning process. Data reduction results in increased capabilities and generalization properties of the learning model and a shorter time of the learning process. It can also help in scaling up to large data sources. The paper proposes an agent-based data reduction approach with the learning process executed...
The paper presents a short overview of the foundations of the Role-Based Access Control Modal Model and its properties. In particular, the translation of these model formulae to the first-order logic formulae in a form of Horn's clauses is analysed. The automation of processes and mechanisms related to access control on the basis of logical automated reasoning and the PROLOG language are described.
Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. This article illustrates several applications of fractional calculus in robot manipulator path planning and control....
In this paper a method for the design of algorithms is presented which use fuzzy techniques in order to achieve a better vagueness treatment. A base of rules will be developed in order to design the algorithms. Data fuzzification problem is solved by using probability density functions and probability distribution functions, whereas data analysis is set out associating, to each one of the analysis rules, a fuzzy set which will be obtained by applying an aggregation function which will be defined...
In this paper a novel method of noise reduction in color images is presented. The new technique is capable of attenuating both impulsive and Gaussian noise, while preserving and even enhancing the sharpness of the image edges. Extensive simulations reveal that the new method outperforms significantly the standard techniques widely used in multivariate signal processing. In this work we apply the new noise reduction method for the enhancement of the images of the so called gene chips. We demonstrate...